arXiv subjects

Yuriy Dementiev

Publications and source records attributed to Yuriy Dementiev.

6 recordsLinked to original sources

arXiv2026

Subexponential Algorithm for High Multiplicity Fair Division of Mixed Instances via Stereometry

We study the problem of computing an envy-free (EF) allocation of $m$ indivisible items among $n$ agents when items come in three distinct types. Each agent holds additive valuations over item types that may be positive (goods), negative (chores), or mixed. We present the first subexponential-time algorithm with running time time $(n \cdot m)^{O(\sqrt{n})}$ that finds an EF allocation whenever one exists, or correctly reports that none exists. Our approach exploits a geometric representation of EF allocations as convex polyhedra in $\mathbb{R}^3$ and applies Miller's planar cycle-separator theorem to recursively decompose the agent set into balanced subgroups. We further extend the algorithm to handle agents whose allocations are fixed in advance, preserving envy-freeness across all agents.

cs.DS↗

arXiv2026

Learning Augmented Exact Exponential Algorithms

The field of learning-augmented algorithms has demonstrated that machine-learned predictions can bypass worst-case lower bounds across a wide range of problems. So far, however, the focus has been almost exclusively on polynomial-time algorithms, where predictions improve competitive ratios, approximation guarantees, or running times. In this paper, we raise the question of whether predictions can push the frontier of exact exponential-time algorithms for NP-hard problems. We answer this question affirmatively by proposing a general approach that augments an entire family of state-of-the-art exact algorithms for a variety of subset selection problems. We show that a noisy predictor that is only marginally better than random guessing suffices to provably reduce the search space, and that the resulting runtime speedup scales smoothly with the prediction quality. Importantly, our algorithms require only pairwise independence of predictions or, alternatively, do not require the knowledge of the predictor's accuracy - both strictly weaker and more realistic settings than typically assumed.

cs.DS↗

arXiv2026

Structural Approach to Guiding a Present-Biased Agent

Time-inconsistent behavior, such as procrastination or abandonment of long-term goals, arises when agents evaluate immediate outcomes disproportionately higher than future ones. This leads to globally suboptimal behavior, where plans are frequently revised or abandoned entirely. In the influential model of Kleinberg and Oren (2014) such behavior is modeled by a present-biased agent navigating a task graph toward a goal, making locally optimal decisions at each step based on discounted future costs. As a result, the agent may repeatedly deviate from initial plans. Recent work by Belova et al. (2024) introduced a two-agent extension of this model, where a fully-aware principal attempts to guide the present-biased agent through a specific set of critical tasks without causing abandonment. This captures a rich class of principal-agent dynamics in behavioral settings. In this paper, we provide a comprehensive algorithmic characterization of this problem. We analyze its computational complexity through the framework of parameterized algorithms, focusing on graph parameters that naturally emerge in this setting, such as treewidth, vertex cover, and feedback vertex set. Our main result is a fixed-parameter tractable algorithm when parameterized by the treewidth of the task graph and the number of distinct (v,t)-path costs. Our algorithm encaptures several input settings, such as bounded edge costs and restricted task graph structure. We demonstrate that our main result yields efficient algorithms for a number of such configurations. We complement this with tight hardness results, that highlight the extreme difficulty of the problem even on simplest graphs with bounded number of nodes and constant parameter values, and motivate our choice of parameters. We delineate tractable and intractable regions of the problem landscape, which include answers to open questions of Belova et al. (2024).

cs.GT↗

arXiv2026

EFX and PO Allocation Exists for Two Types of Goods

We study the problem of fairly and efficiently allocating indivisible goods among agents with additive valuations. We focus on envy-freeness up to any good (EFX) -- an important fairness notion in fair division of indivisible goods. A central open question in this field is whether EFX allocations always exist for any number of agents. While prior work has established EFX existence for settings with at most three distinct valuations (Prakash HV et al. 2025) and for two types of goods (Gorantla, Marwaha, and Velusamy 2023), the general case remains unresolved. In this paper, we extend the existent knowledge by proving that EFX allocations satisfying Pareto optimality (PO) always exist and can be computed in quasiliniear time when there are two types of goods, given that the valuations are positive. This result strengthens the existing work of (Gorantla, Marwaha, and Velusamy 2023), which only guarantees the existence of EFX allocations without ensuring Pareto optimality. Our findings demonstrate a fairly simple and efficient algorithm constructing an EFX+PO allocation.

cs.GT↗

arXiv2024

How to guide a present-biased agent through prescribed tasks?

The present bias is a well-documented behavioral trait that significantly influences human decision-making, with present-biased agents often prioritizing immediate rewards over long-term benefits, leading to suboptimal outcomes in various real-world scenarios. Kleinberg and Oren (2014) proposed a popular graph-theoretical model of inconsistent planning to capture the behavior of present-biased agents. In this model, a multi-step project is represented by a weighted directed acyclic task graph, where the agent traverses the graph based on present-biased preferences. We use the model of Kleinberg and Oren to address the principal-agent problem, where a principal, fully aware of the agent's present bias, aims to modify an existing project by adding or deleting tasks. The challenge is to create a modified project that satisfies two somewhat contradictory conditions. On one hand, the present-biased agent should select specific tasks deemed important by the principal. On the other hand, if the anticipated costs in the modified project become too high for the agent, there is a risk of the agent abandoning the entire project, which is not in the principal's interest. To tackle this issue, we leverage the tools of parameterized complexity to investigate whether the principal's strategy can be efficiently identified. We provide algorithms and complexity bounds for this problem.

cs.GT↗

arXiv2021

Inconsistent Planning: When in doubt, toss a coin!

One of the most widespread human behavioral biases is the present bias -- the tendency to overestimate current costs by a bias factor. Kleinberg and Oren (2014) introduced an elegant graph-theoretical model of inconsistent planning capturing the behavior of a present-biased agent accomplishing a set of actions. The essential measure of the system introduced by Kleinberg and Oren is the cost of irrationality -- the ratio of the total cost of the actions performed by the present-biased agent to the optimal cost. This measure is vital for a task designer to estimate the aftermaths of human behavior related to time-inconsistent planning, including procrastination and abandonment. As we prove in this paper, the cost of irrationality is highly susceptible to the agent's choices when faced with a few possible actions of equal estimated costs. To address this issue, we propose a modification of Kleinberg-Oren's model of inconsistent planning. In our model, when an agent selects from several options of minimum prescribed cost, he uses a randomized procedure. We explore the algorithmic complexity of computing and estimating the cost of irrationality in the new model.

cs.CC↗